GOES MTF Measurements

The acuity of the GOES-I/M Imagers is specified by a Modulation Transfer Function (MTF) test requirement.
Before launch, the GOES MTFs are measured for the visible and infrared channels, and compared to the requirements.
These values are listed in the tables below.

A "MTF" is a fraction - the output amplitude divided by the input amplitude of a sine-wave at a spatial (angular) frequency.

Detector footprints are specified by the angle they project through the telescope.
The highest achievable resolution is one black-white cycle, two footprints wide, called the "Nyquist frequency" = 0.5*(1/footprint).
Image-acuity specifications are written as increasing MTF percentages at 1, 1.5, 2, 4,... times the Nyquist frequency.

For example, the GOES visible detectors have nominal footprints of 1 kilometer at the Equator (28 microradians).
The corresponding Nyquist frequency is 0.5*(1/28urad) = 18,000 cycles-per-radian.
The GOES visible channels are required to have at least 32% MTF at 18,000 Hz/radian (Nyquist), and at least 92% MTF at 4,490 Hz/radian (4 Nyquist).

Most GOES channels pass most of their MTF requirements.
However, the GOES visible channels consistently fail to achieve a reasonably high MTF for the coarsest pattern (four times the Nyquist frequency).
The problem seems to lie with the shiney interior of the visible detector package, which must scatter light by multiple reflections, giving the GOES visible images a somewhat milky quality.
This can be seen in pictures of the edge of the earth, where there is a faint diffuse halo that extends well beyond the 10 kilometer height of the troposphere.
The halo is not a significant problem for normal weather observations, but it does limit the ability to sharpen GOES visible images, or to estimate haze over water.

The following tables list the pre-launch measurement of the average MTF of each GOES Imager channel, along with the requirements.
The middle frequencies are measured at ambient temperatures; they are a few percent more optimistic than the high/low frequency measurements taken in thermal-vac tests.

MTF Measurements for GOES-8

GOES-8 MTF for Channel 1 (0.64 micron)

Frequency (Hz/radian)

NYQUIST SIZE

REQUIRED MTF

MEASURED MTF

18,000

1.0

0.32±0.02

0.40±0.02

13,500

1.5

0.53±0.02

0.60±0.01

9,000

2.0

0.73±0.02

0.75±0.01

4,490

4.0

0.92±0.02

0.82±0.02

Out-of-spec values are listed in red boldface.

GOES-8 MTF for Channel 2 (3.9 micron)

Frequency (Hz/radian)

NYQUIST SIZE

REQUIRED MTF

MEASURED MTF

4,490

1.0

0.22±0.03

0.38±0.01

3,360

1.5

0.39±0.03

0.55±0.02

2,240

2.0

0.63±0.03

0.72±0.01

GOES-8 MTF for Channel 3 (6.7 micron)

Frequency (Hz/radian)

NYQUIST SIZE

REQUIRED MTF

MEASURED MTF

2,240

1.0

0.22±0.03

0.43±0.02

1,690

1.5

0.39±0.03

0.63±0.02

GOES-8 MTF for Channel 4 (11 micron)

Frequency (Hz/radian)

NYQUIST SIZE

REQUIRED MTF

MEASURED MTF

4,490

1.0

0.22±0.03

0.32±0.01

3,360

1.5

0.39±0.03

0.44±0.02

2,240

2.0

0.63±0.03

0.69±0.01

GOES-8 MTF for Channel 5 (12 micron)

Frequency (Hz/radian)

NYQUIST SIZE

REQUIRED MTF

MEASURED MTF

4,490

1.0

0.22±0.03

0.28±0.01

3,360

1.5

0.39±0.03

0.43±0.01

2,240

2.0

0.63±0.03

0.66±0.01

MTF Measurements for GOES-9

GOES-9 MTF for Channel 1 (0.64 micron)

Frequency (Hz/radian)

NYQUIST SIZE

REQUIRED MTF

MEASURED MTF

18,000

1.0

0.32±0.02

0.34±0.04

13,500

1.5

0.53±0.02

0.61±0.01

9,000

2.0

0.73±0.02

0.76±0.01

4,490

4.0

0.92±0.02

0.84±0.04

Out-of-spec values are listed in red boldface.

GOES-9 MTF for Channel 2 (3.9 micron)

Frequency (Hz/radian)

NYQUIST SIZE

REQUIRED MTF

MEASURED MTF

4,490

1.0

0.22±0.03

0.35±0.01

3,360

1.5

0.39±0.03

0.55±0.02

2,240

2.0

0.63±0.03

0.71±0.01

GOES-9 MTF for Channel 3 (6.7 micron)

Frequency (Hz/radian)

NYQUIST SIZE

REQUIRED MTF

MEASURED MTF

2,240

1.0

0.22±0.03

0.38±0.02

1,690

1.5

0.39±0.03

0.56±0.02

GOES-9 MTF for Channel 4 (11 micron)

Frequency (Hz/radian)

NYQUIST SIZE

REQUIRED MTF

MEASURED MTF

4,490

1.0

0.22±0.03

0.30±0.01

3,360

1.5

0.39±0.03

0.45±0.02

2,240

2.0

0.63±0.03

0.63±0.01

GOES-9 MTF for Channel 5 (12 micron)

Frequency (Hz/radian)

NYQUIST SIZE

REQUIRED MTF

MEASURED MTF

4,490

1.0

0.22±0.03

0.30±0.01

3,360

1.5

0.39±0.03

0.45±0.01

2,240

2.0

0.63±0.03

0.64±0.01

North-South MTF Measurements

NOAA only wrote MTF requirements for east-west scan motions.
Nevertheless, it is useful to know the north-south blur to estimate image acuity between scanlines.
ITT's ambient temeprature measurements (i.e. optimistic values by a several percent at high frequencies) are listed below.